TestGardener (version 3.3.6)

surp.fit: Objects resulting for assessing fit of surprisal matrix to surprisal data

Description

This function is called by function smooth.surp() and computes the penalized verstion of the objective function value, its derivative vector and the second derivative matrix, as well as their unpenalized versions. Also returned are alternative fitting objects: the residual matrix, the root-mean-square of the matrix fit, and the entropy value.

Usage

surp.fit(Bvec, surpList)

Value

A named list of class surpFd with these members:

PENSSE

value of the penalized fitting criterion.

DPENSSE

gradient of the penalized fitting criterion.

D2PENSSE

hessian of the fitting criterion.

SSE

value of the error sum of squares.

DSSE

gradient of the error sum of squares.

D2SSE

hessian of the error sum of squares.

DvecSmatDvecB

cross derivative DvecSmatDvecX times DvecXmatDvecB of the surprisal curve and the basis coordinates.

Rmat

residual matrix for the fit to the surprisal matrix.

RMSE

root-mean-squared scalar fit value.

Entropy

entropy of the fit to the data.

Arguments

Bvec

The K by M-1 parameter matrix defining the fit to the data in row-wise column vector format for use with function lnsrch().

surpList

A list object containing objects M, binctr, Sbin, wtvec, Kmat, Zmat and Phimat.

Author

Juan Li and James Ramsay

References

Ramsay, J. O., Li J. and Wiberg, M. (2020) Full information optimal scoring. Journal of Educational and Behavioral Statistics, 45, 297-315.

Ramsay, J. O., Li J. and Wiberg, M. (2020) Better rating scale scores with information-based psychometrics. Psych, 2, 347-360.

See Also

eval.surp, smooth.surp, Sbinsmth

Examples

# Assemble the objects in the list arguments Bmat and surpList
SfdList1 <- Quant_13B_problem_parmList$SfdList[[1]]
Bmat     <- SfdList1$Sfd$coef
binctr   <- Quant_13B_problem_parmList$binctr
M        <- SfdList1$M
Sbasis   <- SfdList1$Sfd$basis
Zmat     <- SfdList1$Zmat
Sbin     <- SfdList1$Sbin
Phimat   <- fda::eval.basis(binctr, Sbasis)
Snbasis  <- Sbasis$nbasis
Kmat     <- matrix(0,Snbasis,Snbasis)
wtvec    <- NULL
Bvec     <- matrix(Bmat, Snbasis*(M-1),1,byrow=TRUE)
#  display coefficient matrix
print(round(Bmat,2))
#  set up argument surpList
surpList <- list(binctr=binctr, Sbin=Sbin, wtvec=wtvec, 
                 Kmat=Kmat, Zmat=Zmat, Phimat=Phimat, M=M)
#  run surp.fit
result <- surp.fit(Bvec, surpList)
print(paste("Error sum of squares =",round(result$SSE,3)))
print(paste("Gradient norm =",round(norm(result$DSSE),5)))
print("Entropy of item = at bin centres")
print(round(result$Entropy,3))